Math 115                                             Name:                          Key                                                     

Quiz 3                                                  September 20, 2013                                        

 

1.  Andy and Terry split a cake by the divider-chooser method.  Andy, the divider, likes chocolate icing twice as much as vanilla.  Show 2 different ways that Andy might split the cake to ensure he gets a “fair” piece. 


1 option is to make each share contain                        Swap 1 choc for 2 white and it is still fair (to Andy)

2 choc, 2 white:           {7,8,1,2} / {3,4,5,6}               for example, {5,6,7,8,1} / {2, 3, 4} is fair

 

2.  Three players, Ali, Bo, and Caz, divide the 13 items shown by the method of markers. 


1       2      3         4        5       6      7        8        9       10     11    12   13

 
 

Which items: go to Ali? 9-13

 

          go to Bo?  1 - 3

 

          go to Caz?   6 -7

 

                      are (initially) left over? 4, 5, 8

 

2b.  According to the rules of this method, how should the leftovers be allocated?  EXPLAIN your answer in a complete English sentence.

 

Since everyone has received a fair share already, no matter what allocation of the leftovers is chose it will still be fair – so it doesn’t matter.

 

 

 

Games

Toys

Clothes

Alex

30

18

12

Brenda

36

16

20

3. 2 sisters, Alex and Brenda, divide some games, some clothes, and some toys by the method of sealed bids. 

The bids (in $) are as follows: 

a.        Find the value of each sister’s fair share

 

Alex, 60/2= $30

            Brenda, 72/2 = $36

 

b.      Determine what items each sister gets.  Then compute the payments in the first settlement, and finally determine the result after the final settlement.

 

Alex gets the toys (value of $18 to her), Brenda gets the games and clothes ($56 to her)

Brenda then pays $20, while Alex takes $12.  There is then an $8 surplus, so each gets $4 from that.  End result:  Alex gets the toys and $16, Brenda gets the game and clothes, and pays $16.